Ubiquity Ch 1-3

I began reading Ubiquity by Mark Buchanan.  My advisor suggested it to me Tuesday when we had our weekly meeting.  I've read through the third chapter and am completely entranced by it.  I tend to fall asleep reading most books or articles, but this book has engaged me greatly.

The book has covered two simple games thus far.  The first is the sand pile game.  Set a rate to drop granules of sand in a pile.  As the sand falls, avalanches of various sizes will occur.  The avalanches occur only if a threshold of instability is introduced by a single new grain.  These regions where this instability exists are called fingers of instability.  The resulting distribution of avalanches follows a power law (log(# of avalanches) v log(size of avalanche) gives a linear distribution...the slope of which determines the power).  The power law suggests there is no typical size of avalanche as would a bell/normal/Gaussian distribution suggests, for example.  This game was introduced by Per Bak, Chao Tang, and Kurt Weisenfeld, although it seems Bak delved much deeper into this than the others from what I gather from Buchanan.

The other game discussed is a game modeling earthquakes.  The game was originally introduced in 1967 by Burridge and Knopoff.  They used a physical model with a setup in one dimension, but didn't find what they were probably hoping for.  Bak and Tang rekindled the idea in 1989 but used a computer simulation in two dimensions.  The game is set up with a ceiling that is allowed to drift.  Connected to the ceiling are rods which are also connected to blocks on a floor.  Between the blocks are springs to connect one block with four neighbors.  The game is then set in motion by drifting the ceiling, as the ceiling moves, the rods bend.  When a rod reaches its limit, the connected block moves one unit.  The springs connected to that block then shift the neighboring blocks by one fourth a unit.  Bak and Tang found this to follow a power law, suggested it described earthquake sizes as being unpredictable, and were excited to show that this game was identical in nature to the sand pile game.  However, others pointed out their model was conservative, unlike real earthquakes which do not transfer all energy into motion.  Instead, some energy is lost in heating the rocks, not moving them.  In 1992 a few other scientists, Olami, Feder, and Christensen redid the Bak and Tang model, but allowed for dissipation of energy.  Their game resulted in matching data from a 1950's study by Gutenburg and Richter in which they found that real earthquakes follow a power law distribution.  Earthquakes have no typical scale since the distribution of earthquake intensity and number of those earthquakes follow a power law distribution, and this is matched by both games.

The next chapters should go into financial markets, wars, and other awesome world events.  I can't wait.
Adam D Scott